In the United States, the Federal Communications Commission (FCC) allows a restricted unlicensed use of ultra-wide bandwidth (UWB) signals for wireless communication systems, “First Report and Order,” Feb. 14, 2002. The UWB signals must be in the frequency range from 3.1 to 10.6 GHz, and have a minimum bandwidth of 500 MHz. The FCC order also limits the power spectral density and peak emissions power of UWB signals to less than −43.1 dBm/MHz.
One modulation method for UWB uses extremely short time pulses, e.g., 1/1,000,000,000 of a second or less, to generate signals with bandwidths greater than 500 MHz which corresponds to a wavelength of about 300 mm. Wireless systems that use short pulses are commonly referred to as impulse radio (IR) systems.
As shown in FIG. 1A, four different modulation techniques are commonly used for IR systems: pulse position modulation (PPM) 11, pulse amplitude modulation (PAM) 12, on-off keying (OOK) 13, and bi-phase shift keying (BPSK) 14.
As an advantage, UWB systems achieve high data rates, and are resistant to multi-path impairments. This is due to large processing gains. Additionally, IR systems enable low cost, low duty cycle, low power transceivers that do not require local oscillators for heterodyning. Because UWB transceivers are primarily implemented in the digital domain, the UWB transceivers can be integrated in a semiconductor chip. In UWB systems, multiple transceivers concurrently share the same spectrum without interference. UWB systems are ideal for short range, high-speed networks in homes, businesses, and educational institutions. Sensor networks can also use UWB transceivers.
A time-hopping (TH) IR is described by M. Win and R. A. Scholtz, “Ultra-Wide Band Width Time-Hopping Spread-Spectrum Impulse Radio for Wireless Multiple-Access Communications,” in IEEE Trans. On Communications, Vol. 48, No. 4 April 2000, pp. 679-691. In that TH-IR system, each bit or symbol is represented by Nf pulses, where Nf is a positive integer. The time to transmit a bit is Ts. This is called the symbol duration. The time Ts is further partitioned into frames Tf, and the frames are partitioned into chips Tc, corresponding typically to a pulse duration. If Nc represents the number of chips in a frame and Nf represents the number of frames in a symbol, then Ts, Tf, and Tc are related byTs=NfTf=NfNcTc.  (1)
FIG. 1B shows the relationship between the symbol time Ts 101, the frame duration Tf 102, and the chip duration Tc 103 for pulses 104 for an example prior art TH-IR waveform 110 for a ‘0’ bit, and a waveform 120 for a ‘1’ bit. Typically, the pulses are spaced pseudo-randomly among the available chips in a frame according to a “time-hopping” code to minimize multi-user interference.
As stated above, the modulation can be binary phase shift keying (BPSK). With BPSK, each bit b is represented as either a positive or negative one, i.e., b∈{−1, 1}. The transmitted signal has the form
                                          s            ⁡                          (              t              )                                =                                    ∑                              i                =                1                            ∞                        ⁢                                          ∑                                  j                  =                  1                                                  N                  f                                            ⁢                                                h                                      i                    ,                    j                                                  ⁢                                  b                                      ⌊                                          i                      /                                              N                        f                                                              ⌋                                                  ⁢                                  p                  ⁡                                      (                                          t                      -                                              j                        ⁢                                                                                                  ⁢                                                  T                          f                                                                    -                                                                        c                          j                                                ⁢                                                  T                          c                                                                                      )                                                                                      ,                            (        2        )            where cj represents the jth value of the TH code, in a range {0, 1, . . . , Nc−1}, and b is the ith modulation symbol. Additionally, an optional sequence denoted as hi,j can be applied to each pulse in the transmitted signal to ‘shape’ the spectrum of the transmitted signal and to reduce spectral lines. The sequence, hi,j, is called a polarity scrambling sequence with values of either +1 or −1. Different amplitudes are also possible to further shape the spectrum.
FIG. 2 shows a conventional coherent TH-IR receiver 200. The receiver includes an automatic gain control (AGC) unit 210 coupled to an amplifier 220 that is connected to the receive antenna 230. The receiver also includes synchronization 240, timing control 250, channel estimation 260, MMSE equalizer 270, and decoder 280 units. Rake receiver fingers 290 input to an adder 295. Each rake receiver finger includes a pulse sequence generator, correlator and weight combiner. The rake receiver fingers reduce multipath interference.
An appropriate duration of the frame needs to be selected. A short frame duration decreases multiple access interference (MAI), and can also increase performance in the presence of timing jitter, as described by S. Gezici, H. Kobayashi, H. V. Poor, and A. F. Molisch, “Effect of timing jitter on the tradeoff between processing gains,” Proc. ICC 2004, pp. 3596-3600, 2004. On the other hand, interframe interference (IFI) can occur when the frame duration is shorter than a maximum excess delay of the channel impulse response. In conventional TH-IR systems, the frame duration is fixed and cannot be changed.
Therefore, it is desired to select adaptively the frame duration.